A new algorithm for computing asymptotic series
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Symbolic asymptotics: multiseries of inverse functions
Journal of Symbolic Computation
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Necessary and sufficient conditions for the existence of limits of the form lim"("x","y")"-"("a","b")f(x,y)/g(x,y) are given, under the hypothesis that f and g are real analytic functions near the point (a,b), and g has an isolated zero at (a,b). The given criterion uses a constructive version of Hensel@?s Lemma which could be implemented in a computer algebra system in the case where f and g are polynomials with rational coefficients, or more generally, with coefficients in a real finite extension of the rationals. A high level description of an algorithm for determining the existence of the limit as well as its computation is provided.